38 lines
1.7 KiB
Python
38 lines
1.7 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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d, h = 200, 1200 # pixel density (= image width) and image height
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n, r = 8000, 10000 # number of iterations and escape radius (r > 2)
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a = -.743643887037158704752191506114774 # https://mathr.co.uk/web/m-location-analysis.html
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b = 0.131825904205311970493132056385139 # try: a, b, n = -1.748764520194788535, 3e-13, 800
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x = np.linspace(0, 2, num=d+1)
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y = np.linspace(0, 2 * h / d, num=h+1)
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A, B = np.meshgrid(x * np.pi, y * np.pi)
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C = 8.0 * np.exp((A + B * 1j) * 1j) + (a + b * 1j)
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Z, dZ = np.zeros_like(C), np.zeros_like(C)
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D = np.zeros(C.shape)
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for k in range(n):
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M = Z.real ** 2 + Z.imag ** 2 < r ** 2
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Z[M], dZ[M] = Z[M] ** 2 + C[M], 2 * Z[M] * dZ[M] + 1
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N = abs(Z) > 2 # exterior distance estimation
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D[N] = np.log(abs(Z[N])) * abs(Z[N]) / abs(dZ[N])
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plt.imshow(D.T ** 0.05, cmap=plt.cm.nipy_spectral, origin="lower")
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plt.savefig("Mercator_Mandelbrot_map.png", dpi=200)
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X, Y = C.real, C.imag # zoom images (adjust circle size 100 and zoom level 20 as needed)
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R, c, z = 100 * (2 / d) * np.pi * np.exp(- B), min(d, h) + 1, max(0, h - d) // 20
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fig, ax = plt.subplots(2, 2, figsize=(12, 12))
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ax[0,0].scatter(X[1*z:1*z+c,0:d], Y[1*z:1*z+c,0:d], s=R[0:c,0:d]**2, c=D[1*z:1*z+c,0:d]**.5, cmap=plt.cm.nipy_spectral)
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ax[0,1].scatter(X[2*z:2*z+c,0:d], Y[2*z:2*z+c,0:d], s=R[0:c,0:d]**2, c=D[2*z:2*z+c,0:d]**.4, cmap=plt.cm.nipy_spectral)
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ax[1,0].scatter(X[3*z:3*z+c,0:d], Y[3*z:3*z+c,0:d], s=R[0:c,0:d]**2, c=D[3*z:3*z+c,0:d]**.3, cmap=plt.cm.nipy_spectral)
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ax[1,1].scatter(X[4*z:4*z+c,0:d], Y[4*z:4*z+c,0:d], s=R[0:c,0:d]**2, c=D[4*z:4*z+c,0:d]**.2, cmap=plt.cm.nipy_spectral)
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plt.savefig("Mercator_Mandelbrot_zoom.png", dpi=100)
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